The Mediterranean Basin, located in a transition zone between the temperate and rainy climate of central Europe and the arid climate of North Africa, is considered a major hotspot of climate change, subject to water scarcity and drought. In this work, dry and wet spells have been analyzed in the Wadi Cheliff basin (Algeria) by means of annual precipitation observed at 150 rain gauges in the period 1970–2018. In particular, the characteristics of dry and wet spells (frequency, duration, severity, and intensity) have been evaluated by means of the run theory applied to the 12-month standardized precipitation index (SPI) values. Moreover, in order to detect possible tendencies in the SPI values, a trend analysis has been performed by means of two non-parametric tests, the Theil–Sen and Mann–Kendall test. The results indicated similar values of frequency, severity, duration, and intensity between the dry and the wet spells, although wet events showed higher values in the extreme. Moreover, the results of the trend analysis evidenced a different behavior between the northern side of the basin, characterized by a negative trend in the 12-month SPI values, and the southern side, in which positive trends were detected.